Why not ?
CE is the done that doing the civil works for plant upgrading, new projects, etc.
Pet also have dedicated CE team for offshore/onshore projects 

yes of course.

for offshore platforms, you can work as structural engineer (design, transportation & installation, integrity, fabrication engineer), or pipeline engineer.

for onshore, again you can work as structural engineer and civil engineer for all the onshore plants, buildings, etc.

generally you can specialise in project planning, QA&QC, project management, cost control, contract management, procurement, etc.

in short, there are plenty of opportunities for civil engineering graduates in oil & gas.